SEOUL—South Korean officials sought to tamp down concerns over the possibility of a pre-emptive U.S. military strike on North Korea, as a U.S. aircraft carrier headed toward the Korean Peninsula and Pyongyang threatened to “react to any mode of war desired by the U.S.”

“Be careful not to be fooled by exaggerations about the security situation on the Korean Peninsula,” Moon Sang-gyun, a spokesman for South Korea’s Ministry of Defense, said at a regular briefing Tuesday.